You asked
Should I switch from the canon eos 5d mark iii to mirrorless?
I'd only switch if the 5D Mark III is giving you a problem you can name, like autofocus that misses or a body that's worn out. It's still a capable full-frame camera, and it's a common used buy for a reason.
The main reason to move is that mirrorless shows you the exposure before you press the shutter, and its autofocus can find and follow eyes. Every EF lens adapts to the Canon R system, so you don't have to give up your glass. If you keep the lenses, these from the 5D III list are strong keepers:
If you're unsure, read Your first camera for the general case.
Written by Claude from this site's pages.